Chapter 11.2, Problem 4CYU

To determine

To Find: The correct option out of the given options for the given question.

Answer to Problem 4CYU

The correct option is D) 12 sides.

Explanation of Solution

Given information:

The sum of all the interior angles of the given polygon is ${1800}^0$ .

Concept and Formula Used:

The formula used here is the formula for the sum of all the interior angles of a given polygon of ‘n’ sides.

Sum of all the interior angles of a polygon = ${180}^0\times \left(n-2\right)$

Calculation:

As the given polygon has sum of all its interior angles ${1800}^0$ , so we have

  $\begin{array}{l}{1800}^0={180}^0\times \left(n-2\right)\\ \frac{{1800}^0}{{180}^0}=n-2\\ 10=n-2\\ 10+2=n\\ n=12\end{array}$

So, the correct option is D) 12 sides.

Conclusion:

The correct option is D) 12 sides.